The many null distributions of person fit indices

This paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fittingitems may be removed, this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting ofk symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called ability parameter, although our results are equally valid for Rasch scales measuring other attributes.As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.The authors express their gratitude to the reviewers and to many colleagues for comments on an earlier version.     

Food and amphetamine self-administration by baboons: effects of alternatives.

The effects of the availability of an alternative reinforcer on responding maintained by food pellets or fluid solutions were examined in 6 adult male baboons (Papio cynocephalus anubis). During daily 23-hr experimental sessions, baboons had concurrent access to both food pellets and fluid, with responding maintained under fixed-ratio schedules of reinforcement that varied between the two commodities. The fixed-ratio requirement, or cost, for pellets was increased when (a) no fluid, (b) a dilute dextrose vehicle, (c) 0.002 mg/kg d-amphetamine, or (d) 0.004 mg/kg d-amphetamine was available. When given nonrestricted concurrent access to food pellets and amphetamine at minimal cost (FR 2), baboons self-administered sufficient amphetamine to decrease pellet intake. Increasing the response requirement for pellets decreased pellet intake at a similar rate regardless of the available fluid and increased fluid intake in a variable manner among baboons such that there were no statistically significant increases in fluid intake. In contrast, when access to pellets was restricted to 70% of maximal intake under nonrestricted conditions, increasing pellet cost decreased pellet intake and increased fluid intake more rapidly when the high amphetamine dose was available. Thus, amphetamine was more effective as an economic substitute for pellets when access to pellets was restricted. The response cost for vehicle and both amphetamine concentrations was increased when baboons had nonrestricted and restricted access to pellets. Increasing the response requirement for fluid delivery decreased intake of all three fluids similarly under both pellet-access conditions. The results indicate that substitution between commodities with minimal commonalities can be studied under controlled laboratory conditions and is dependent upon reinforcement schedule and commodity restrictions.     

Response-independent Events In The Behavior Stream

The metaphor of the behavior stream provides a framework for studying the effects of response-independent food presentations intruded into an environment in which operant responding of pigeons was maintained by variable-interval schedules. In the first two experiments, response rates were reduced when response-independent food was intruded during the variable-interval schedule according to a concomitantly present fixed-time schedule. These reductions were not always an orderly function of the percentage of response-dependent food. Negatively accelerated patterns of key pecking across the fixed-time period occurred in Experiment 1 under the concomitant fixed-time variable-interval schedules. In Experiment 2, positively and negatively accelerated and linear response patterns occurred even though the schedules were similar to those used in Experiment 1. The variable findings in the first two experiments led to three subsequent experiments that were designed to further illuminate the controlling variables of the effects of intruded response-independent events. When the fixed and variable schedules were correlated with distinct operanda by employing a concurrent fixed-interval variable-interval schedule (Experiment 3) or with distinct discriminative stimuli (Experiments 4 and 5), negatively accelerated response patterns were obtained. Even in these latter cases, however, the response patterns were a joint function of the physical separation of the two schedules and the ratio of fixed-time or fixed-interval to variable-interval schedule food presentations. The results of the five experiments are discussed in terms of the contributions of both reinforcement variables and discriminative stimuli in determining the effects of intruding response-independent food into a stream of operant behavior.     

The Development of the Toddler Behavior Screening Inventory

The purpose of the present study was to develop the Toddler Behavior Screening Inventory (TBSI) for rapidly assessing maternal reports of toddler behavior problems. The TBSI is a 40-item measure intended for use by pediatricians, psychologists, and other child-care professionals. A group of mothers (n = 312) rated the initial 93-item TBSI in terms of behavior frequency and parental perception of the behavior as problematic. Following item elimination, 40 items were retained due to being both frequent and problematic at all toddler age levels. Data were obtained with a new sample of mothers (n = 581) and showed the TBSI to possess good reliability and validity.     

Data Smoothing: Prediction of Human Behavior, Detection of Behavioral Patterns, and Monitoring Treatment Effectiveness in Single-Subject Behavioral Studies

Data-smoothing can be particularly useful in predicting human behavior, detecting behavioral patterns, and monitoring treatment effectiveness in highly variable single-subject behavioral experiments that cannot be determined by only visual inspection of their graphs. Using an example from the applied behavior analytic literature, the use of moving-average and exponential data-smoothing aided the detection of the unique behavioral patterns of a child with autism across different treatments. Furthermore, the utility of the data-smoothing procedures to monitor and control the effectiveness of an intervention is discussed. The ease of their calculations suggest use of data-smoothing by behavior analysts whenever the effects of particular interventions are questionable.     

Should the behavioral sciences become more pragmatic? The case for functional contextualism in research on human behavior

Although societal need for behavioral science research is enormous, current research practices seem to be inefficient vehicles for producing knowledge that guides practical action. Many of our most popular theories provide little direct guidance for application. They focus on the development of models of the relationships among organismic events such as attitudes, self-efficacy expectations, and behavior, but pay little or no attention to the contextual influences on behavior. Such research is in keeping with a long-standing mechanistic tradition in psychology. We propose a version of contextualism as an alternative paradigm for the behavioral sciences. According to this paradigm, theories and research are evaluated in terms of their contribution to the prediction and influence of behavior. Basic research organized to pursue this goal has a direct bearing on how behavioral phenomena can be changed for practical purposes. Conversely, applied research contributes to basic understanding of the determinants of psychological phenomena.     

EMERGENCE OF REINFORCER PREFERENCE AS A FUNCTION OF SCHEDULE REQUIREMENTS AND STIMULUS SIMILARITY

Tustin (1994) recently observed that an individual's preference for one of two concurrently available reinforcers under low schedule requirements (concurrent fixed-ratio [FR] 1) switched to the other reinforcer when the schedule requirements were high (concurrent FR 10). We extended this line of research by examining preference for similar and dissimilar reinforcers (i.e., those affecting the same sensory modality and those affecting different sensory modalities). Two individuals with developmental disabilities were exposed to an arrangement in which pressing two different panels produced two different reinforcers according to progressively increasing, concurrent-ratio schedules. When two dissimilar stimuli were concurrently available (food and a leisure item), no clear preference for one item over the other was observed, regardless of the FR schedules in effect (FR 1, 2, 5, 10, and 20). By contrast, when two similar stimuli were concurrently available (two food items), a clear preference for one item emerged as the schedule requirements were increased from FR 1 to FR 5 or FR 10. These results are discussed in terms of implications for conducting preference assessments and for selecting reinforcers to be used under training conditions in which response requirements are relatively high or effortful.     

Courteous service: Its assessment and modification in a human service organization

We evaluated strategies to increase behaviors associated with courteous provision of service by 3 staff members of a human service agency. Training included written instructions, practice, and performance feedback. A lottery procedure was introduced to maintain courteous service after training. The results of a multiple baseline design across the 3 participants showed marked increases in courteous behaviors following training. These effects were maintained at 3-, 5-, and 8-month follow-ups. Consumers' satisfaction with service also increased. These findings suggest that simple training and reinforcement procedures can enhance courtesy afforded those who receive service from public and nonprofit organizations.     

ANALYSIS OF A HIGH-PROBABILITY INSTRUCTIONAL SEQUENCE AND TIME-OUT IN THE TREATMENT OF CHILD NONCOMPLIANCE

This study evaluated the effectiveness of high-probability requests and time-out as treatments for noncompliance that appeared to be maintained by contingent attention in 2 developmental normal children. The introduction of high-probability requests increased compliance for 1 child but not the other. Time-out was effective with both children, and improvements in compliance were maintained at an 8-week follow-up.     

ACHIEVING AND MAINTAINING COMPLIANCE WITH THE KETOGENIC DIET

The ketogenic diet, a treatment for intractable epilepsy, is rarely initiated because it requires strict compliance with a diet that is perceived to be unpalatable. In a case study of a 15-year-old girl with uncontrolled epilepsy, we used a stimulus-choice procedure to assess relative preferences of 33 foods from the diet and to develop two treatments based on Premack's principle. The results of a multielement analysis showed that both treatments increased dietary compliance. Compliance was maintained with generalization of treatment across settings, and was associated with a 40% reduction in seizures.